need mathematica's help for exploring a certain type of mapping
- To: mathgroup at smc.vnet.net
- Subject: [mg68559] need mathematica's help for exploring a certain type of mapping
- From: "Nabeel Butt" <nabeel.butt at gmail.com>
- Date: Wed, 9 Aug 2006 04:20:56 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Dear Users,
I need to use mathematica's graphics to explore a certain
kind of problem.The following theorem is not yet proven nor disproven and
mathematica might proof useful in disproving it though.
Hypothesis:If a mapping from R^2->R^3 is unit distance preserving then it
must be an isometry.
The real issue at hand is for mathematica to generate a mapping that
preserves unit distance but is not an isometry so in the process disproving
the theorem.
The real problem is that R^2 consists of infinite points and it might
not be possible to check all of them.What i suggest is that you apply the
unit preserving maps to special type of figures in R^2 like the circumfrence
of the circle,square,isoceles triangle etc.
Any ideas are welcome.Thanks in advance.
regards,
Nabeel
--
Nabeel Butt
LUMS,Lahore